Search: “finite-fields”

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Efficient Branch-and-Bound Testing and Verification of zkVMs

ZEBRA verifies zkVM constraint systems via branch-and-bound cardinality counting, finding 11 zero-day bugs across five real-world zkVMs and running 51.5x faster than SMT verification.

ZEBRA reduces zkVM correctness to a solution-set cardinality problem requiring that each constraint system admit exactly one valid execution trace, eliminating redundancies like null-row padding and non-deterministic permutations before counting. It lifts analysis from finite-field witnesses to an integer interval lattice, exploiting that constraints across 5 real-world zkVMs use only 14.0% of theoretical connectivity capacity on average, enabling tight interval propagation. A parallel branch-and-bound search produces concrete counterexamples or certifies absence of violations within a bounded region. ZEBRA discovers 11 zero-day bugs (6 independently confirmed, 3 fixed), is 51.5x faster than SMT-based verification, and verifies 16.5 percentage points more instances.

arXiv cs.CR·Sep 14, 04:35 UTC · 2d agoResearch

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Unsolved Problem by Fields Medalist Breached by Two High School Students

Two high school students used Claude Opus 5 and GPT-5.6 Sol to help solve an open Lorentzian polynomials problem, posting a 75-page arXiv proof.

Aayush Bathija and Prince Rohatgi of Oak Park High School, mentored by UCLA postdoc Daniel Soskin, published the 75-page paper 'Bounded Ratios for Lorentzian Polynomials' (arXiv 2609.05341), solving an open problem in Fields Medalist June Huh's Lorentzian polynomial theory. The main structural theorem extends bounded coefficient-ratio characterization from quadratic to arbitrary-degree polynomials via discrete convexity conditions. The students used Claude Opus 5 and GPT-5.6 Sol for exploration and proof ideas but independently verified all arguments; the result follows an open letter from 25 Fields Medalists voicing concerns about AI's impact on mathematical rigor.

Hacker News · security·Sep 14, 12:23 UTC · 2d agoAI researchHN 22↑ · 19 comments

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Characterizing Language Generation in the Limit: Finite Witnesses and a Separation-Width Hierarch

New work characterizes language generation in the limit via finite witnesses, proves a full separation-width hierarchy, and formalizes all results in Lean.

The paper fully characterizes when language generation in the limit is possible for arbitrary families over a countable universe: each target must admit a finite positive witness such that targets activated by any finite sample share an infinite common intersection. It defines positive separation width and proves every level of the resulting hierarchy occurs, with countable families admitting singleton witnesses and unions of families with infinite common cores requiring unbounded finite witnesses. The characterization, a universal normalization, and a diagonal capture lemma are machine-checked in the Lean proof assistant, with the development maintained on GitHub.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:54 UTC · 6d agoAI research1

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On APN Functions with Boomerang Uniformity One over $\mathbb F_{3^n}$: Differential and Boomerang Spectra and CCZ-Inequivalence

Cryptographic construction yields infinite APN function families with boomerang uniformity one over odd-characteristic fields, proving CCZ-inequivalence to power functions.

For q=3^n with odd n>1, every sign-switch of a perfect nonlinear Dembowski-Ostrom polynomial is proven APN with boomerang uniformity one or two, attaining uniformity one for (q-3)/2 parameters. This gives the first general construction of infinite APN families achieving boomerang uniformity one over odd-characteristic finite fields. The authors determine common differential and complete boomerang spectra, ruling out CCZ equivalence with power and Ness-Helleseth binomials, and exhibit three pairwise CCZ-inequivalent PN functions for infinitely many n, with the smallest degree n=45.

arXiv cs.CR·Sep 8, 16:19 UTC · 7d agoResearch

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Augustinian BabyLM: What Ostensive Definition Can and Cannot Teach a Small Language Model

Study shows visually grounded token embeddings in a small masked LM persist through training and improve object-property knowledge, but escape standard BabyLM benchmarks.

The paper implements ostensive definition for a small DeBERTa masked language model trained on 10M words, seeding visually grounded tokens with embeddings derived from labeled image regions before training. Visual initialization leaves a persistent, seed-replicated advantage on object-property knowledge (COMPS) and a corpus-tailored Visual-Property Swap benchmark covering color, material, size, and shape, but has no effect on most BabyLM grammar benchmarks. Synthetic grounding of previously unseeded words causally transfers the advantage to exactly those words.

arXiv cs.AI / cs.LG / cs.CL·Sep 10, 17:43 UTC · 5d agoAI research

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Beyond the Turing threshold: Productive grammars generate essentially undecidable languages

A theoretical paper designs formal grammars that emulate Post's productive sets, generating languages that are provably beyond Turing decidability.

The paper elaborates on Emil Post's productive sets, which are not even semi-computable, and builds formal grammars that emulate their construction over natural numbers. The resulting languages are shown to be essentially undecidable, placing them beyond Turing decidability. This is pure computability and formal language theory with limited direct security relevance.

arXiv cs.CR·Sep 10, 11:20 UTC · 6d agoResearch1

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Nonmaximal sums of maximally monotone operators under Rockafellar's constraint qualification

Mathematical paper constructs counterexamples on c0 and l1 disproving Rockafellar's conjecture that sums of maximally monotone operators remain maximally monotone.

The authors build counterexamples where two maximally monotone operators satisfy the interior-domain condition yet their sum is not maximally monotone, refuting Rockafellar's sum conjecture. One counterexample is constructed on c0 and another on l1 with its usual norm. A general construction theorem computes the monotone polar of a class of graphs, gives necessary and sufficient conditions for maximal monotonicity, and shows how a positive rank-one perturbation yields a nonmaximal sum.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:26 UTC · 6d agoAI research

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Benign Loss Landscapes Can Coexist with Worst-Case Hardness

Theory paper shows tree tensor networks contain worst-case hard targets yet benign loss landscapes, with difficulty arising from degenerate saddles.

The paper studies tree tensor networks (TTNs), which generalize deep linear networks and Tucker decompositions and embed arbitrary read-once Boolean formulas. It proves that every local minimum that is minimum-norm is global for every realizable target, so bad local minima do not distinguish typical from worst-case problems. Instead, learning difficulty arises from high-order degenerate saddle points caused by rank-deficiency, illustrated via a parity function case study, linking landscape geometry to computational hardness.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 16:57 UTC · 4d agoAI research

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A Note on Sphere Packing Bounds for Tuple Lattice Sieving

Proves upper bounds on k-irreducible unit vector set rates, yielding nearly tight asymptotics relevant to tuple lattice sieving in cryptanalysis.

The paper bounds the maximal asymptotic rate of k-irreducible sets of unit vectors via spherical code packing bounds. It shows R_k is sandwiched between (1/2 - o(1)) log2(k)/k and (1 + o(1)) log2(k)/k for large k. These almost-tight bounds inform subexponential complexity analyses of tuple lattice sieving, which underpins security estimates for lattice-based cryptography.

arXiv cs.CR·Sep 8, 03:20 UTC · 8d agoResearch

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Implementing a White-Box Undetectable Backdoor for Random Fourier Features

Researchers implement Goldwasser's CLWE-based undetectable backdoor for Random Fourier Features models in numpy/scipy, confirming practical realizability with no detectable differences from clean models.

The paper provides an end-to-end implementation of the Goldwasser et al. white-box undetectable backdoor for models trained with the Random Fourier Features algorithm, using only numpy and scipy. It derives two samplers for the core GP_d(b_k) distribution: a rejection-sampling proxy and an exact closed-form sampler verified against its analytic form. Statistical indistinguishability tests covering weight-space and functional black-box comparisons found no detectable difference between backdoored and clean models across sparsity ratios. The underlying lattice hardness reduction was not reproduced, and the work demonstrates the threat is realizable with commodity scientific-computing tools rather than specialized cryptographic infrastructure.

arXiv cs.CR·Sep 14, 22:18 UTC · 1d agoResearch

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ZGCM-1: A Fully Open and Extremely Efficient Foundation Model for Math and Agentic Search

ZGCM-1 is a fully open 7B foundation model with 256K context that stays competitive with frontier models on math reasoning and agentic search.

ZGCM-1 is a fully open 7B dense foundation model trained from scratch using an efficiency-focused recipe: interleaved gated sliding-window and full attention, a stable FP8 Muon optimizer, and MDP-based mid-training with context scaling across 16K, 64K, and 256K. On mathematical reasoning and agentic search suites it remains competitive with much larger frontier models such as Qwen3-235B-A22B and GLM-5.1. The recipe yields a ~4.2x improvement in 16K pre-training time-to-loss, and all weights, checkpoints, training code, data recipes, and W&B logs are open-sourced.

Hugging Face daily papers·Sep 10, 20:00 UTC · 5d agoModel release

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MathKernel: An evidence-aware multi-engine mathematics kernel and MCP server

MathKernel is an open-source, evidence-aware multi-engine mathematics kernel that exposes verification workflows to AI agents via an MCP server.

MathKernel, published on GitHub, is a mathematics kernel that combines multiple computation engines with evidence-aware outputs. It ships as an MCP server, enabling AI agents and coding assistants to perform and verify calculations. The project drew moderate attention on Hacker News.

Hacker News · security·Sep 7, 00:21 UTC · 9d agoAI tools & infraHN 36↑ · 5 comments

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OpenArch – PyTorch implementations of modern LLM architectures

OpenArch provides PyTorch reference implementations of modern LLM architectures for developers and researchers.

OpenArch is a GitHub project offering PyTorch implementations of modern large language model architectures. The repository attracted 43 points and 7 comments on Hacker News. It targets developers and researchers who want readable, runnable versions of current LLM architectures.

Hacker News · AI·Sep 14, 07:55 UTC · 2d agoAI tools & infraHN 43↑ · 7 comments

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EFI Pairs Without One-Way Puzzles: Oracle Separations from Communication Complexity

Theorists build a classical oracle where one-way puzzles fail yet EFI pairs survive, separating two candidate minimal assumptions of quantum cryptography.

The paper constructs a single classical oracle relative to which one-way puzzles do not exist, even with an unbounded verifier, while an EFI pair survives every classical-query distinguisher holding advice, making one superposition query at the end. Security is proven by reducing adversary knowledge to communication complexity for Vector-in-Subspace, with the superposition query bounded using random matrix theory. Relative to the oracle, quantum polynomial time offers no advantage on tasks with classical inputs and outputs and there is no proof of quantumness, separating the leading minimal assumptions of quantum cryptography.

arXiv cs.CR·Sep 10, 17:54 UTC · 5d agoResearch

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🔬“We have foundation models for language, not for physics” — Anima Anandkumar, Bren Professor of Computing

Caltech professor Anima Anandkumar discusses Neural Operators and FourCastNet for physics modeling, arguing inductive biases beat pure token scaling.

Anima Anandkumar, Bren Professor at Caltech and co-founder of Accelerated Understanding, describes Fourier Neural Operators that learn in frequency and spherical-harmonic domains to model weather, fusion, and fluid or heat flow. Her team built FourCastNet 3, a global weather model competitive with physics-based simulations that runs on consumer-grade GPUs. She also introduced TorchLean, a framework for writing PyTorch-style networks inside the Lean proof assistant for formal verification, and was appointed to the United Nations Scientific Advisory Board. She argues physical domains resist scaling due to tiny datasets and context lengths in the hundreds of billions, so progress comes from built-in structure and physical priors.

Latent Space·Aug 26, 15:15 UTC · 21d agoAI research1

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Differential Privacy Meets Fixed Parameter Tractability: Algorithms and Lower Bounds

Theory paper combines differential privacy with fixed-parameter tractable encoders, improving approximation guarantees for combinatorial optimization and proving new lower bounds.

The paper studies combinatorial optimization under epsilon-differential privacy within the implicit encoder-decoder framework of Gupta et al. (SODA 2010), generalizing it to allow fixed-parameter tractable encoders. This circumvents approximation barriers inherent to polynomial-time algorithms and yields improved guarantees for fundamental combinatorial optimization problems. The authors establish the first representation-independent lower bounds: assuming a non-uniform variant of the Gap Exponential Time Hypothesis, no epsilon-DP encoder-decoder pair can achieve certain approximation guarantees with a subexponential-time decoder for sufficiently small epsilon. Representation-dependent lower bounds are also provided for larger epsilon.

arXiv cs.CR·Sep 11, 07:13 UTC · 5d agoResearch

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Nearly Tight Rademacher Bounds for Sparsely Activated Neural Networks

Theory paper derives nearly tight Rademacher complexity bounds for sparsely activated one-hidden-layer ReLU networks.

Building on Awasthi et al. (COLT 2024), the authors bound statistical complexity for networks where each input activates at most k of s hidden units. A support-preserving cover and normalized chaining argument remove the explicit dimension factor, with matching lower bounds up to logarithms. They also derive agnostic minimax excess-risk bounds of order min{1, sqrt(s/(km))} for a normalized bounded loss and show bias bounds comparable to WR restore worst-case rates even on domains where sparsity holds globally.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:53 UTC · 7d agoAI research

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Searching for New Physics with Reinforcement Learning

Researchers apply reinforcement learning to identify SMEFT operators explaining particle physics anomalies, reproducing and improving known CDF W-mass results.

The paper introduces a reinforcement learning method to search the large Standard Model Effective Field Theory (SMEFT) operator space for explanations of measurement anomalies. It was validated on the CDF W-mass anomaly, reproducing and improving known results, then applied to a harder multi-anomaly scenario. RL efficiently navigates complex loop-level operator correlations that bias human-driven phenomenological analysis.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 16:07 UTC · 6d agoAI research

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AI models' written reasoning steps correspond to distinct internal patterns, a new study finds

KAIST and Naver AI Lab researchers show LLM reasoning steps like extraction and computation map to distinct activation patterns, strongest in middle layers.

Researchers at KAIST and Naver AI Lab defined eight recurring reasoning operations, including extraction, decomposition, formula recall, deduction, and computation, and showed they correspond to separable activation patterns in Qwen2.5-7B, Qwen3-8B, and Gemma4-31B on math tasks, with GPT-5 labeling solution segments. The separation peaks in middle layers, holds even when a computation step produces a wrong answer, and goes beyond surface-level token choice. Findings replicated on Llama-3-8B, and classifiers trained on Qwen3-8B transferred to GPQA-Diamond and MATH-500. The authors note that using internal states for error detection or mid-generation steering remains future work.

The Decoder·Sep 12, 13:39 UTC · 4d agoAI research2

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Distance generalization in transformers: why bother with positional encoding?

arXiv study uses synthetic delay-copy tasks to show how RoPE, ALiBi, NoPE and training data diversity affect transformers' distance generalization.

The paper studies distance generalization in transformers: extrapolating when inter-token distances change between training and inference while context length stays fixed. Using two synthetic delay-copy tasks with finite source-recall distances, the authors test models on unseen delays. They investigate whether positional encodings such as RoPE and ALiBi outperform no positional encoding (NoPE), how the diversity of training distances affects performance, and when distance transfer learning is positive or negative.

arXiv cs.AI / cs.LG / cs.CL·Sep 10, 17:57 UTC · 5d agoAI research2

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Unfold The World: Factorize 4D Properties in Reinforcing Spatial Reasoning

FactoSR factorizes 4D spatial reasoning into XY, Z, and T reinforcement-learning sub-objectives, boosting VLM performance on VSI-Bench by 5.9% and All-Angles-Bench by 4.5%.

Researchers present FactoSR, a factorized reinforcement learning framework that decomposes world-consistent reasoning into planar correspondence, depth consistency, and temporal reversibility sub-objectives. Optimizing these verifiable constraints turns the ill-posed projection recovery problem into tangible reasoning steps. Evaluations show gains of 5.9% on VSI-Bench and 4.5% on All-Angles-Bench for 3D and 4D reasoning, arguing VLMs' spatial bottleneck stems from training on 2D projections versus latent 3D geometry and temporal continuity.

Hugging Face daily papers·Sep 2, 20:00 UTC · 13d agoAI research

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Large Universe Subset Predicate Encryption with IND-CCA Security (with Constant-size Ciphertext and Keys)

New construction achieves first large-universe subset predicate encryption with IND-CCA security and constant-size ciphertexts and keys under subgroup decision assumptions.

The paper proposes the first large-universe subset predicate encryption scheme achieving IND-CCA security with both constant-size ciphertexts and constant-size secret keys. Prior large-universe constructions by Chatterjee and Mukherjee either achieved only restricted selective security with constant sizes or adaptive security with attribute-dependent ciphertext size, and none achieved CCA security. The new construction is proven selectively secure under standard subgroup decision problems. Black-box transformations yield the first CCA-secure WIBE and WKD-IBE with constant-size ciphertexts and keys.

arXiv cs.CR·Sep 14, 10:02 UTC · 2d agoResearch

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Kaininja: Extending Native 3D Generators to the Part Level

KaiNinja extends TRELLIS.2 native 3D generation to part-level assets via a dual-volume O-Voxel representation, cutting whole-object Chamfer distance by 40%.

KaiNinja extends the TRELLIS.2 native 3D generator to produce part-level assets instead of one fused mesh, enabling downstream editing, rigging, and simulation. A dual-volume form of the O-Voxel representation solves the problem that a single volume cannot represent interfaces where two parts touch. The model needs no segmentation network, is partly trained on LLM-agent-authored part data, lowers whole-object Chamfer distance by 40%, and raises strict part F-score by 16% versus other part-generation pipelines.

Hugging Face daily papers·Sep 13, 20:00 UTC · 2d agoAI research

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Towards a Deterministic Math Solver for Clinical Language Models

Paper shows handing arithmetic to a deterministic Python solver beats direct model calculation at 32B but not reliably at 7B on MedCalc-Bench.

Researchers test a Program-Solve interface where clinical LLMs write case-specific Python executed by a restricted local solver instead of doing arithmetic directly. On MedCalc-Bench Verified (1,100 cases, 55 calculators), Qwen2.5-32B-AWQ scored 90.53% with solver handoff versus 83.47% with direct arithmetic (+7.05 points), while Qwen2.5-7B gained an unreliable +3.29 points with a confidence interval spanning zero. The authors audited the benchmark against clinical guidelines and flagged 16 of 55 calculators for version, use, or coefficient concerns.

Hugging Face daily papers·Sep 8, 20:00 UTC · 7d agoAI research

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Claude Mythos 5 is coming to Tenable One, powering the new “Adversary View”

Tenable will integrate Anthropic's Claude Mythos 5 into Tenable One, launching Adversary View to surface exploitable vulnerability chains from scan data.

Tenable announced it is bringing Anthropic's Claude Mythos 5 into the Tenable One Exposure Management Platform, extending its Project Glasswing research work with Anthropic. The first capability, Tenable One Adversary View, will use the model's adversarial reasoning over raw scanner evidence, plugin output, live connections and low-confidence signals to identify viable vulnerability chains and ranked defensive actions. Customers will act on results through Tenable Hexa AI. Availability details for Adversary View are expected in the coming weeks; no customer deployment exists yet.

Tenable Blog·Sep 8, 17:21 UTC · 7d agoTools1

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Leading mathematicians fear AI is making their field dumber, and warn the rest of us is next

Twenty-five Fields Medal winners, including Terence Tao, warn AI companies' benchmark-driven approach to mathematics is misaligned with the discipline's purpose of understanding.

In a joint statement, 25 Fields Medal winners including Terence Tao, Peter Scholze, and Maryna Viazovska warn that AI systems solving major open problems at machine speed undermine conceptual understanding and raise severe attribution and plagiarism questions. The statement lands amid a controversy accusing OpenAI of training math models to beat researchers to a rumored partial solution of a Millennium Prize Problem. The signatories describe a general threat to intellectual work across professions and call for urgent action by mathematicians, AI companies, and society, while not seeking a ban.

The Decoder·Sep 12, 08:28 UTC · 4d agoAI industry1

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Perplexity Details Its GPU Embedding Stack: How Ivy, Tulip and ROSE Serve pplx-embed

Perplexity details its GPU embedding serving stack (Ivy, Tulip, ROSE), which reuses LLM prefill/decode kernels, CUDA graphs, and LazyTensors to cut launch overhead.

Perplexity engineers published a deep dive on the serving infrastructure behind pplx-embed, used across Perplexity Search and its API platform. The stack comprises Ivy (Rust HTTP gateway), Tulip (gRPC scheduling and batching), and ROSE (Runtime-Optimized Serving Engine), which reuses LLM prefill and decode kernels rather than running a separate embedding engine. Optimizations include whole-model CUDA graphs with lazy capture and a LazyTensor abstraction that overlaps CPU batch preparation with in-flight GPU work. Benchmarks are reported against vLLM v0.22.0 in BF16, with FlashAttention 4 generally fastest but FlashInfer 3 winning on Qwen-based models at very long sequence lengths.

MarkTechPost·Sep 6, 03:20 UTC · 10d agoAI tools & infra1

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Quenched Ensemble Sampling

Quenched Ensemble Sampling generalizes nested sampling's hard energy constraint to repulsive potentials, traversing first-order phase transitions where tempering fails.

Quenched Ensemble Sampling generalizes nested sampling's hard energy constraint into a family of repulsive potentials at the energy boundary, preserving monotone energy descent while making the constrained target amenable to scalable gradient-based kernels. On synthetic phase-transition models it estimates marginal likelihood and draws posterior samples across first-order transitions where popular alternatives such as tempering fail. Applications include marginal likelihood estimation for Bayesian neural network architecture comparison and partition function estimation in a high-dimensional continuous lattice field theory.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:16 UTC · 1d agoAI research1

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Type Diversity Enables Transformers to Generalise Compositionally

Researchers show lexical-versus-structural compositional generalization gaps in Transformers stem from type diversity imbalance in datasets, not architectural limits.

The paper argues that Transformers' difficulty with structural compositional generalization is an artifact of low structural type diversity in prior benchmark datasets rather than an architectural limitation. Using Grammatical Framework, the authors create linguistically diverse variants of COGS and SLOG. They find type diversity correlates with compositional generalization equally in lexical and structural test cases, contradicting previous claims that compound divergence explains task difficulty.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 17:59 UTC · 4d agoAI research

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Recursive Code World Models: Building Complex Worlds through Recursive Scene Programs

RCWM reconstructs complex 3D worlds as executable code from a single image using recursive scene programs with global-local-global solver recursion.

The paper introduces Recursive Code World Models, coupling a Recursive Scene Program representation with a recursive construction solver for image-to-3D-world reconstruction. Each solver call establishes the whole scene, recursively reconstructs unresolved parts, and revisits the whole to refine composition, while a vision-language coding agent compares reference images with scene renders to guide refinement. RCWM outperforms prior code-based image-to-scene reconstruction methods, and ablations show deeper recursive calls improve fine-scale reconstruction.

Hugging Face daily papers·Sep 9, 20:00 UTC · 6d agoAI research1

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Proximity Gaps for Gabidulin Codes and Applications

Researchers prove proximity-gap bounds for rank-metric and Gabidulin codes, enabling the first polynomial commitment scheme framework based on rank-metric error-correcting codes.

The paper proves every linear rank-metric code admits a proximity gap for deltas up to (d-1)/(3n) with error at most q^(e+1)/q^m, and improves the gap to (d-1)/(2n) for Gabidulin codes with error at most 10q^(n-1)/q^m, matching bounds for Reed-Solomon codes. A constructed infinite family of constant-rate Gabidulin codes shows the (d-1)/(2n) bound is tight, and a counterexample establishes a lower bound on the error at the d/(3n) gap. Applications include an IOPP for interleaved Gabidulin codes adapted from the Ligero IOPP and a q-linearized polynomial commitment scheme adapted from Ligero-based PCS, reportedly the first PCS framework based on rank-metric codes.

arXiv cs.CR·Sep 9, 07:45 UTC · 7d agoResearch

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